\newproblem{lay:4_3_3}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 4.3.3}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Ana Pe\~na Gil, Jan. 19th 2014} \\}{}

  % Problem statement
	Determine whether the set $B=\{(1,0,-3),(3,1,-4),(-2,-1,1)\}$ is a basis or not for 
	$\mathbb{R}^3$. If it is not,
	determine if it is linearly independent.\\
}{
  % Solution
	$B$ has three linearly dependent vectors because if we form the matrix 
	\[A=\begin{pmatrix} 1 & 3 & -2 \\ 0 & 1 & -1 \\ -3 & -4 & 1\end{pmatrix}\] 
	its determinant $\det\{A\} = 0$, which means that A is formed by linearly dependent vectors.
	
	Since $B$ has 3 linearly dependent vectors, it does not span $\mathbb{R}^3$ and it is not, 
	therefore, a basis for $\mathbb{R}^3$. \\
}
\useproblem{lay:4_3_3}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
